When i render active scene with the mesh that converted from the hand writing picture there is nothing to be seen in the render window
“Convert to Geometry, Path” will convert your grease pencil drawing into a Path and that path should be selectable and visible in the 3D View window (if you hide the grease pencil lines). However, paths are not normally visible in renders since they have no width.

To make the path visible in the render simply select it, select the Curve properties in the right-hand properties panel (it’s the one with a curve with a white dot at each end), scroll down to Geometry and increase the Bevel Depth. This will add some renderable geometry to the path. Adjust the other settings to get the desired effect (eg, change Fill in the Shape panel to Full) and optionally add a Subdivision Surface modifier to get a rounded stroke.